FLY or SKY ATTACKEARTHQUAKEDRAGON TAIL or DRAGON RUSHRETURN or RECOVER

fly or sky attack is your choice of stab. fly hurts a bit, but has that two turn prediction thing. while sky attack is a bit risky after you lose your power herb. and is especially risky with a choice band.
earthquake is good coverage. dragon tail and dragon rush cover the many dragons of ubers. low accuracy is something you'll face with both of them. return is for choice band for some extra neutral hits, while recover is for power herb.

Swagger + Punishment for Power and Main Attacking.
Thunder Wave for crippling.

Dragon Tail can be used with Deoxys-D, who can set up Spikes 3x and Stealth Rock.
Aerial Ace for STAB and hits everytime.
Bulldoze for lowering speed, but not needed with Thunder Wave.
Dragon Rush for Power.

Lugia is one of the few effective Pokemon with a moveset like the following:

Dragon Tail
Rest
Sleep Talk
Whirlwind

The strengths of this set are dragon tail attacks that can land first due to 110 base speed and sleep talk, whirlwind to break bulky substitutes, and rest to recover HP, set up sleep talk, and engage multiscale. This moveset works very well with leftovers and when stealth rocks or other entry hazards are in play.

Well, to be fair I haven't played too much Smogon Ubers, but I have used this set many times against competitively oriented Uber Teams against friends, as well as the Uber Infested Battle spot. Still. The thing I can tell you is that if you're running a Calm Mind Lugia, you really don't want to run max HP as opposed to Special Attack. This is because Lugia's Special Attack is low and Aeroblast has low PP, so having to use it excessively will lead to bad results. With max investment in Sp. Attack, Lugia is similar to Max HP Calm Mind Arceus and could therefore be seen as a replacement; Lugia is a bit slower but is bulkier overall and can hold leftovers, though because Arceus holds a plate Judgement will hit harder than Aeroblast.. But that "Bulk" is not to be excused--With a Calm Mind and Multiscale up, Lugia has over 1,000 Special Defense and nearly 600 Defense, so it's not going anywhere. In contrast, t +1 Lugia has 418 Sp. Attack, which offers decent offensive presence. Earth Power offers great coverage alongside Aeroblast, but Psyshock is another move to consider, as it has secondary STAB and can bypass an enemy's high Sp. Defense, such as when facing a Calm Mind Arceus.